Finite Group Databasebeta

← #30620442

Subgroups — #30620442

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#446C211yesmaximal, characteristic
2#21462338C211yesmaximal, characteristic
3#21462003C211yesmaximal, characteristic
4#21462002C211yesmaximal, characteristic
5#21462001C211yesmaximal, characteristic
6#21461999C211yesmaximal, characteristic
7#21461999C211yesmaximal, characteristic
8#21461997C211yesmaximal, characteristic
9#21461690C211yesmaximal, characteristic
10#21461690C211yesmaximal, characteristic
11#21461688C211yesmaximal, characteristic
12#21461591C211yesmaximal, characteristic
13#21461591C211yesmaximal, characteristic
14C4×#14519840C211yesmaximal, characteristic
15#557×D61C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19#16840812—21no—
20D61⋊(C4⋊C8)C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22D61⋊(C4⋊C8)C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27#16840721C2211yescharacteristic
28#16840721C2211yescharacteristic
29C4×D61⋊C8C2211yescharacteristic
30(C2×#6923)⋊Q8—21no—
31#16840711—21no—
32#16840711—21no—
33#16840708C2211yescharacteristic
34#16840706C2211yescharacteristic
35#16840706C2211yescharacteristic
36C4⋊C4×#6923—21no—
37C4×C4⋊#6923C2211yescharacteristic
38C4×C4⋊#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840491C411yescharacteristic, complemented
53#16840490—21no—
54#16840490C411yescharacteristic, complemented
55#16840489—21no—
56#16840489—21no—
57#16840489C411yescharacteristic, complemented
58#16840489C411yescharacteristic, complemented
59#16840488C411yescharacteristic, complemented
60#16840488C411yescharacteristic, complemented
61#16840487—21no—
62#16840487C411yescharacteristic, complemented
63C4⋊Q8×D61—21no—
64C4⋊Q8×D61C2211yescharacteristic
65#125×D61—21no—
66#125×D61—21no—
67#125×D61C2211yescharacteristic
68#125×D61C2211yescharacteristic
69C4×Q8×D61—21no—
70C4×Q8×D61C2211yescharacteristic
71C4×Q8×D61C2211yescharacteristic
72C4×Q8×D61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C61×#557C411yescharacteristic, complemented
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78C2×D61⋊C8C2311yescharacteristic
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844—21no—
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94#14519840—22no—
95#14519840—22no—
96#14519840—22no—
97#14519840Q814yescomplemented
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101#14519832—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111C2×Q8×D61—21no—
112C2×Q8×D61D411yescharacteristic
113C2×Q8×D61C2311yescharacteristic
114#14519777—21no—
115#14519777C2×C411yescharacteristic
116#14519776—21no—
117#14519776—21no—
118#14519776—21no—
119#14519776—21no—
120#14519776—21no—
121#14519776C2×C411yescharacteristic
122#14519776C2×C411yescharacteristic
123#14519775—21no—
124#14519775—21no—
125#14519775—21no—
126#14519769—21no—
127#14519769—21no—
128#14519769C2×C411yescharacteristic
129#14519769C2×C411yescharacteristic
130#14519768—21no—
131#14519768—21no—
132#14519768—21no—
133#14519768—21no—
134#14519768C2×C411yescharacteristic
135#14519768C2×C411yescharacteristic
136#14519768C2×C411yescharacteristic
137#14519768C2×C411yescharacteristic
138#14519767—21no—
139#14519767—21no—
140#14519767—21no—
141#14519767—21no—
142#14519767—21no—
143#14519767—21no—
144#14519767—21no—
145#14519767—21no—
146#14519767—21no—
147#14519767—21no—
148#14519767—21no—
149#14519767—21no—
150Q8×Dic61—21no—
151Q8×Dic61C2×C411yescharacteristic
152Q8×Dic61C2×C411yescharacteristic
153Q8×Dic61C2×C411yescharacteristic
154Q8×Dic61D411yescharacteristic
155C4×Dic122—21no—
156C4×Dic122—21no—
157C4×Dic122—21no—
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122—21no—
161C4×Dic122C2×C411yescharacteristic
162C4×Dic122C2×C411yescharacteristic
163C4×Dic122C2×C411yescharacteristic
164C4×Dic122C2×C411yescharacteristic
165C4×Dic122C2×C411yescharacteristic
166C4×Dic122C2×C411yescharacteristic
167#14519742—21no—
168#14519742—21no—
169#14519742—21no—
170#14519742—21no—
171#14519742—21no—
172#14519742—21no—
173#14519742C2×C411yescharacteristic
174#14519742C2×C411yescharacteristic
175#14519742C2×C411yescharacteristic
176#14519742D411yescharacteristic
177#14519742D411yescharacteristic
178#14519742D411yescharacteristic
179C4⋊C4×D61—21no—
180C4⋊C4×D61—21no—
181C4⋊C4×D61—21no—
182C4⋊C4×D61—21no—
183C4⋊C4×D61—21no—
184C4⋊C4×D61—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61D411yescharacteristic
188C4⋊C4×D61D411yescharacteristic
189C4⋊C4×D61D411yescharacteristic
190C4⋊C4×D61C2311yescharacteristic
191C4⋊C4×D61C2311yescharacteristic
192C4⋊C4×D61C2311yescharacteristic
193C42×D61—21no—
194C42×D61—21no—
195C42×D61—21no—
196C42×D61C2311yescharacteristic
197C42×D61C2311yescharacteristic
198C42×D61C2311yescharacteristic
199C4⋊Q8×C61—21no—
200C4⋊Q8×C61C2×C411yescharacteristic
201#125×C61—21no—
202#125×C61—21no—
203#125×C61C2×C411yescharacteristic
204#125×C61C2×C411yescharacteristic
205C4×Q8×C61—21no—
206C4×Q8×C61C2×C411yescharacteristic
207C4×Q8×C61C2×C411yescharacteristic
208C4×Q8×C61C2×C411yescharacteristic
209C4×Q8×C61C2×C411yescharacteristic
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61C22⋊C411yescharacteristic
216C2×Q8×C61C22×C411yescharacteristic
217Q8×D61—21no—
218Q8×D61—21no—
219Q8×D61—41no—
220Q8×D61—41no—
221Q8×D61—42no—
222Q8×D61—42no—
223Q8×D61C2×Q812yes—
224Q8×D61#4112yes—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2411yescharacteristic
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122C22⋊C411yescharacteristic
241C2×Dic122C22⋊C411yescharacteristic
242C2×Dic122C22⋊C411yescharacteristic
243C2×Dic122C22×C411yescharacteristic
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C4⋊#6923—21no—
249C4⋊#6923—21no—
250C4⋊#6923—21no—
251C4⋊#6923—21no—
252C4⋊#6923—21no—
253C4⋊#6923—21no—
254C4⋊#6923—21no—
255C4⋊#6923—42no—
256C4⋊#6923—81no—
257C4⋊#6923C2×Q812yes—
258C4×#6923—42no—
259C4×#6923—81no—
260C4×#6923—81no—
261D61⋊C8—21no—
262D61⋊C8—21no—
263D61⋊C8—21no—
264D61⋊C8—21no—
265D61⋊C8—21no—
266D61⋊C8—21no—
267D61⋊C8—21no—
268D61⋊C8C2×Q812yes—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C22⋊C411yescharacteristic
278C4⋊C4×C61C22⋊C411yescharacteristic
279C4⋊C4×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C42×C61—21no—
284C42×C61—21no—
285C42×C61—21no—
286C42×C61C22×C411yescharacteristic
287C42×C61C22×C411yescharacteristic
288C42×C61C22×C411yescharacteristic
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61C22⋊C411yescharacteristic
298C4⋊Dic61C22⋊C411yescharacteristic
299C4⋊Dic61C22⋊C411yescharacteristic
300C4⋊Dic61C22×C411yescharacteristic
301C4⋊Dic61C22×C411yescharacteristic
302C4⋊Dic61C22×C411yescharacteristic
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327#11758196C22⋊C411yescharacteristic
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—21no—
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61C22×C411yescharacteristic
338C4×Dic61C22×C411yescharacteristic
339C4×Dic61C22×C411yescharacteristic
340C4×Dic61C2×D411yescharacteristic
341C4×Dic61C2×D411yescharacteristic
342C4×Dic61C2×D411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C4×Dic61C2×D411yescharacteristic
345C4×Dic61C2×D411yescharacteristic
346C22×D61C22×D411yescharacteristic
347C2×#6923—22no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359Q8×C61—21no—
360Q8×C61—41no—
361Q8×C61—42no—
362Q8×C61C4×Q812yes—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C23×C411yescharacteristic
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C22×D411yescharacteristic
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—21no—
394C4×D61—21no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—21no—
399C4×D61—41no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61C22×Q811yescharacteristic
406C4×D61C2×#4111yescharacteristic
407C4×D612−1+411yescharacteristic
408C4×D612−1+411yescharacteristic
409Dic122—21no—
410Dic122—22no—
411Dic122—22no—
412Dic122—41no—
413Dic122—41no—
414Dic122—41no—
415Dic122—42no—
416Dic122—42no—
417Dic122—42no—
418Dic122C4×Q812yes—
419#92420—22no—
420#92420—41no—
421#92420—41no—
422#92420—41no—
423#22527—611nomaximal, Sylow
424C22×C61C22×C22⋊C411yescharacteristic
425C2×D61#54811yescharacteristic
426C2×D61D4×Q811yescharacteristic
427C2×D61#57511yescharacteristic
428C2×D61#57511yescharacteristic
429C2×D61#57711yescharacteristic
430C2×D61#57811yescharacteristic
431#6923—42no—
432#6923—81no—
433#6923—81no—
434#6923—81no—
435C4×C61—22no—
436C4×C61—21no—
437C4×C61—21no—
438C4×C61—21no—
439C4×C61—21no—
440C4×C61—21no—
441C4×C61—21no—
442C4×C61—41no—
443C4×C61—41no—
444C4×C61—41no—
445C4×C61C2×C4×Q811yescharacteristic
446C4×C61#51911yescharacteristic
447Dic61—22no—
448Dic61—21no—
449Dic61—21no—
450Dic61—21no—
451Dic61—21no—
452Dic61—21no—
453Dic61—21no—
454Dic61—41no—
455Dic61—41no—
456Dic61—41no—
457Dic61#54811yescharacteristic
458Dic61D4×Q811yescharacteristic
459C2×#557—611no—
460C2×#446—611no—
461#2355—611no—
462#1993—611no—
463#1992—611no—
464#1991—611no—
465#1989—611no—
466#1989—611no—
467#1987—611no—
468#1805—611no—
469#1805—611no—
470#1803—611no—
471#1763—611no—
472#1763—611no—
473C4×#103—611no—
474C2×C61Q8×C22⋊C411yescharacteristic
475C2×C61#289611yescharacteristic
476C2×C61#289811yescharacteristic
477D61#337111yescharacteristic
478D61#337711yescharacteristic
479D61#338811yescharacteristic
480D61#339011yescharacteristic
481#557—611no—
482#557—611no—
483#557—611no—
484#557—611no—
485#557—611no—
486#557—611no—
487#557—611no—
488#557—1221no—
489#557—1221no—
490#557—1221no—
491#557—1221no—
492#557#692311yescharacteristic, complemented
493C2×C4⋊Q8—611no—
494C2×C4⋊Q8—1221no—
495C2×#125—611no—
496C2×#125—611no—
497C2×#125—1221no—
498C2×#125—1221no—
499C2×C4×Q8—611no—
500C2×C4×Q8—611no—
501C2×C4×Q8—611no—
502C2×C4×Q8—611no—
503C2×C4×Q8—1221no—
504#446—1221no—
505#446—1221no—
506#446—1221no—
507#446—1221no—
508C2×C4⋊C8—611no—
509C2×C4⋊C8—611no—
510C2×C4⋊C8—611no—
511C2×#103—611no—
512C2×#103—611no—
513C2×#103—611no—
514C2×#103—611no—
515C2×#97—611no—
516C2×#97—611no—
517C2×C4×C8—611no—
518#391—1221no—
519#387—1221no—
520#387—1221no—
521#384—611no—
522#382—611no—
523#382—611no—
524C4×C4⋊C4—611no—
525C4×C4⋊C4—611no—
526C4×C4⋊C4—611no—
527C4×C4⋊C4—1221no—
528#340—611no—
529#340—611no—
530#340—611no—
531#340—611no—
532#340—611no—
533#340—611no—
534#340—611no—
535#340—611no—
536#340—611no—
537#340—611no—
538#340—611no—
539#340—611no—
540C61#2252711yescharacteristic, complemented, Sylow
541C22×Q8—611no—
542C22×Q8—611no—
543C22×Q8—1221no—
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548C4⋊Q8—21no—
549C4⋊Q8—611no—
550C4⋊Q8—611no—
551C4⋊Q8—611no—
552C4⋊Q8—1221no—
553C4⋊Q8—1221no—
554C4⋊Q8—1221no—
555C4⋊Q8—1221no—
556C4⋊Q8—1221no—
557C4⋊Q8—1221no—
558C4⋊Q8—1221no—
559C4⋊Q8—1221no—
560C4⋊Q8—1221no—
561C4⋊Q8C2×#692311yescharacteristic
562#125—21no—
563#125—21no—
564#125—611no—
565#125—611no—
566#125—611no—
567#125—611no—
568#125—611no—
569#125—611no—
570#125—1221no—
571#125—1221no—
572#125—1221no—
573#125—1221no—
574#125—1221no—
575#125—1221no—
576#125—1221no—
577#125—1221no—
578#125—1221no—
579#125—1221no—
580#125—1221no—
581#125—1221no—
582#125—1221no—
583#125—1221no—
584#125—1221no—
585#125—1221no—
586#125—1221no—
587#125—1221no—
588#125C2×#692311yescharacteristic
589#125C2×#692311yescharacteristic
590C4×Q8—21no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—611no—
596C4×Q8—611no—
597C4×Q8—611no—
598C4×Q8—611no—
599C4×Q8—611no—
600C4×Q8—611no—
601C4×Q8—611no—
602C4×Q8—611no—
603C4×Q8—611no—
604C4×Q8—611no—
605C4×Q8—611no—
606C4×Q8—611no—
607C4×Q8—1221no—
608C4×Q8—1221no—
609C4×Q8—1221no—
610C4×Q8—1221no—
611C4×Q8—1221no—
612C4×Q8—1221no—
613C4×Q8—1221no—
614C4×Q8—1221no—
615C4×Q8—1221no—
616C4×Q8—1221no—
617C4×Q8—1221no—
618C4×Q8—1221no—
619C4×Q8—1221no—
620C4×Q8C2×#692311yescharacteristic
621C4×Q8C2×#692311yescharacteristic
622C4×Q8C2×#692311yescharacteristic
623C4×Q8C2×#692311yescharacteristic
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—1221no—
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1221no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4—1221no—
641C2×C4⋊C4—1221no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4—1221no—
644C2×C42—611no—
645C2×C42—611no—
646C2×C42—611no—
647C2×C42—1221no—
648C2×C42—1221no—
649C2×C42—1221no—
650C2×C42—1221no—
651C2×C42—1221no—
652C2×C42—1221no—
653C4⋊C8—1221no—
654C4⋊C8—1221no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659#103—614no—
660#103—1222no—
661#103—1222no—
662#103—1222no—
663#97—1221no—
664#97—1221no—
665#97—1221no—
666#97—1221no—
667C4×C8—1221no—
668C4×C8—1221no—
669#95—1221no—
670#95—1221no—
671#95—1221no—
672#95—1221no—
673#95—1221no—
674#95—1221no—
675#95—1221no—
676C2×Q8—21no—
677C2×Q8—611no—
678C2×Q8—611no—
679C2×Q8—611no—
680C2×Q8—612no—
681C2×Q8—612no—
682C2×Q8—611no—
683C2×Q8—1221no—
684C2×Q8—1221no—
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8—1221no—
688C2×Q8—1221no—
689C2×Q8—2441no—
690C2×Q8—2441no—
691C2×Q8—2442no—
692C2×Q8—2442no—
693C2×Q8C22⋊#692311yescharacteristic
694C2×Q8C22×#692311yescharacteristic
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C2×C8—612no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—611no—
737C4⋊C4—611no—
738C4⋊C4—611no—
739C4⋊C4—612no—
740C4⋊C4—611no—
741C4⋊C4—611no—
742C4⋊C4—611no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—4881no—
778C4⋊C4—2442no—
779C4⋊C4C22⋊#692311yescharacteristic
780C4⋊C4C22⋊#692311yescharacteristic
781C4⋊C4C22⋊#692311yescharacteristic
782C4⋊C4C22×#692311yescharacteristic
783C4⋊C4C22×#692311yescharacteristic
784C4⋊C4C22×#692311yescharacteristic
785C42—21no—
786C42—21no—
787C42—21no—
788C42—611no—
789C42—611no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—1221no—
798C42—1221no—
799C42—1221no—
800C42—1221no—
801C42—1221no—
802C42—1221no—
803C42—1221no—
804C42—1221no—
805C42—1221no—
806C42—4881no—
807C42—4881no—
808C42—2442no—
809C42C22×#692311yescharacteristic
810C42C22×#692311yescharacteristic
811C42C22×#692311yescharacteristic
812C23—611no—
813Q8—21no—
814Q8—41no—
815Q8—42no—
816Q8—612no—
817Q8—1222no—
818Q8—1222no—
819Q8—1221no—
820Q8—2441no—
821Q8—2441no—
822Q8—2441no—
823Q8—2442no—
824Q8—2442no—
825Q8—2442no—
826Q8Q8×#692312yes—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—611no—
836C2×C4—611no—
837C2×C4—611no—
838C2×C4—611no—
839C2×C4—611no—
840C2×C4—611no—
841C2×C4—611no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1221no—
857C2×C4—1222no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4C2×C22⋊#692311yescharacteristic
879C2×C4C2×C22⋊#692311yescharacteristic
880C2×C4C2×C22⋊#692311yescharacteristic
881C2×C4C2×C22⋊#692311yescharacteristic
882C2×C4C2×C22⋊#692311yescharacteristic
883C2×C4C2×C22⋊#692311yescharacteristic
884C2×C4C23×#692311yescharacteristic
885C8—1222no—
886C8—2441no—
887C8—2441no—
888C8—2441no—
889C22—611no—
890C22—611no—
891C22—611no—
892C22—611no—
893C22—611no—
894C22—611no—
895C22C22×C22⋊#692311yescharacteristic
896C4—22no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—21no—
903C4—41no—
904C4—41no—
905C4—41no—
906C4—611no—
907C4—611no—
908C4—1222no—
909C4—1221no—
910C4—1221no—
911C4—1221no—
912C4—1221no—
913C4—1221no—
914C4—1221no—
915C4—4881no—
916C4—4881no—
917C4—4881no—
918C4—2442no—
919C4—2441no—
920C4—2441no—
921C4—2441no—
922C4C2×Q8×#692311yescharacteristic
923C4#1684083011yescharacteristic
924C2—611no—
925C2—611no—
926C2—611no—
927C2—611no—
928C2Q8×C22⋊#692311yescharacteristic
929C2#2146243911yescharacteristic
930C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#557C4
socleC22×C61C22×C22⋊C4
prime radicalC22×D61C22×D4
cosocleC2×C4×D61C24
hypercenter#557#6923
hypocenterC61#22527
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
52. #16840491C4semidirect
54. #16840490C4semidirect
57. #16840489C4semidirect
58. #16840489C4semidirect
59. #16840488C4semidirect
60. #16840488C4semidirect
62. #16840487C4semidirect
74. C61×#557C4semidirect
97. #14519840Q8semidirect
492. #557#6923semidirect
540. C61#22527semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D61⋊#4462
#214623382
#214620032
#214620022
#214620012
#214619992
#214619972
#214616902
#214616882
#214615912
C4×#145198402
#557×D612
#2252761